Children of Loki

Trickster giant-turned-god Loki caused a lot of mayhem in Norse mythology. Sometimes an ally, sometimes an enemy, sometimes his pranks were harmless, sometimes they lead to murder. Loki had quite a few offspring, and as one might guess they were a varied bunch.

Fenrir

Loki sired three monstrous beasts by a giantess named Angrboda: Fenrir, Hel, and Jormungand. All three were foretold to bring about great disaster, and so were all stolen away by the gods. Fenrir was brought back to Asgard and proved to be impossibly vicious from puppyhood, and only the god Tyr dared go near and feed the wretched warg. Much to the gods dismay Fenrir grew rapidly, and so it was decided the monstrous wolf was to be bound. Using his pride against him, the gods challenged Fenrir to break the two fetters they had made. However he broke through both, so the gods turned to dwarves to fashion a third. Using bizarre materials like the footsteps of a cat and breath of a fish, they fashioned Gleipnir. While incredibly thin, Gleipnir held strong and Fenrir found himself unable to break free. In revenge, he bit off Tyr's hand. Unwilling to defile holy ground with death, the gods thrust a sword into the bound Fenrir's jaws to prevent further attacks.

At some point Fenrir had two wolf sons, Skoll and Hati Hrodvitnisson ("Hrodvitnir" is an alternate name for Fenrir, thus "Hrodvitnisson" is essentially "Fenrir's son"), who chase the Sun and Moon.

Fenrir will ultimately break free of Gleipnir in the Ragnarok and devour Odin, though will himself fall to Vidar's blade.

Hel

Loki's only daughter, Hel is described as physically looking half dead and half alive. The gods cast cast Hel into the underworld and charged her with caring for those that died from sickness, age, or anything else besides glorious battle. Hel named her new home after herself and made the afterlife as dismal as she could.

When the god Baldr was murdered his soul went to Hel, and when the other gods begged her to release him Hel demanded that everything in existence must weep for Baldr. The gods nearly succeeded, but Loki (the culprit behind Baldr's death in the first place) in the form of a giantess refused to mourn and thus kept Baldr dead.

Jörmungandr

The venomous serpent Jörmungandr was tossed into the sea, where he thrived and grew so large he encircled the entire world, thus earning the name Midgard Serpent ("Midgard" being Norse for 'world,' specifically the human's world).

Jörmungandr often came into conflict with the god Thor. The giant king Utgarda-Loki (no, not Loki in disguise or anything, just another giant that happens to share the name) turned the serpent into a gigantic cat and challenged Thor to lift him, an impossible task even for Thor, though the god made impressive effort. Later on during a fishing trip, Thor hooked Jörmungandr using a cow's head as bait. The two began to fight but were stopped by Thor's assistant Hymir. The Midgard Serpent and God of Thunder will get their chance to duke it out in the Ragnarok. Thor will fell Jörmungandr with his hammer, but will himself fall to the serpent's poison immediately after.

Narvi

(Also known as Nari or Narfi)

Vali

Loki had two sons by the goddess Sigyn, and both were used by the gods in an elaborate punishment for Loki for orchestrating Baldr's murder. They changed Narvi's brother Vali into a ravenous, wolf-like monster, who immediately ripped his unfortunate sibling to shreds. The gods then used poor Narvi's entrails to bind Loki to stone slabs while a snake dribbled its poison onto the trickster's eyes. What became of Vali after is unknown.

Odin also had a son called Vali, born purely to kill Hod for his unwitting part in Baldr's death. It is entirely likely that the two Valis are one and the same and that Loki/Sigyn son is simply a translation error.

Sleipnir

Not all of Loki's brood have miserable lives. Sleipnir went on to become the greatest of all horses and Odin's personal steed. The circumstances of his birth, though, are rather... infamous.

Early on when Asgard was just being built, a stonemason offered to construct a wall for the gods, asking for the sun, the moon, and the goddess Freya in return. Loki convinced the gods to agree, though only if the stonemason could do the impossible and build it with three seasons and without any man's help. The stonemason, taking advantage of Loki's poor choice of words, brought in his stallion Svadilfari and was finishing the wall three days before the deadline. The gods, not wanting to lose the deal, blamed Loki for the mess and charged him with fixing it. Loki changed himself into a mare and "distracted" Svadilfari, preventing the stonemason from finishing. The stonemason then tried taking Freya by force, but was promptly killed by Thor.

Some time later Loki himself gave birth to Sleipnir. Never a dull day with the god of mischief!